Or,
In my experience, both sides are wrong.
The psoas shouldn’t be looked at through the lens of its muscle action (primary hip flexion), rather, it should be looked at from the point of view of its muscle function (stability of the lumbar spine).
The psoas has a broad origin that spans the entirety of the lumbar spine. A lumbar spine which has no structural stability like it’s thoracic counterpart, and is heavily reliant on muscles to stabilize.
So rather than attempting to remedy a tight psoas by just stretching or just strengthening, you might want to increase your efforts in stabilizing the lumbar spine and “core” muscle groups in order to expedite the process.
The most effective intervention for a tight hip flexor is to further your efforts in resisting forces through all three planes of the lumbar spine. (flexion/extension, lateral flexion, rotation). This could be as simple as implementing the Mcgill Big three or check out my article Muscle Doc's Big(gest) Three Core Movements for Strength and Performance.
Stay Strong,
Jordan